Chamber Matching of Semiconductor Manufacturing ... - IEEE Xplore

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 4, JULY 2012

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Chamber Matching of Semiconductor Manufacturing Process Using Statistical Analysis Tian-Hong Pan, David Shan-Hill Wong, and Shi-Shang Jang

Abstract—Tools or chambers at a single step are designed to perform the same processing in semiconductor industry. In practice, tools or chambers differ and do not process lots identically. The ability to achieve consistent performance of wafer across the entire toolset is critical to developing and maintaining a high yield. In this paper, a statistical method is proposed to diagnose any reasonable difference between golden and inferior chambers that are classified in terms of end-of-line quality of wafer. Key features of the sensor-variable profiles are mined out to determine the causes of chamber mismatching in the manufacturing process. The method not only employs well-known statistical analysis techniques of discrimination and regression, but also presents a synopsis of analysis results in the chart of R2 statistics versus p-value. This framework provides a systematic method of drawing inference from the available evidence without interrupting the normal process operation. The proposed concept is illustrated by an electroplating process in a local fabrication unit.

Y α

APC FDA FDC IQR MFC PCA PCs QC RtR SPC

Uniformity of the electroplated layer process wafer. Significance level. ABBREVIATIONS Advance process control. Fisher discriminant analysis. Fault detection and classification. Interquartile test. Mass flow controller. Principle component analysis. Principle components. Quality control. Run-to-run control. Statistical process control.

Index Terms—Chamber matching, F -test, interquartile test (IQR-test), R2 statistics, semiconductor manufacturing.

n Q1 Q3 R2 s x x ¯

MAJOR challenge for semiconductor industry lies in the need to continuously improve the overall quality of its final product. In terms of the wafer fabrication area, the yield of wafer is the final evaluation indicator, but it is affected by variability of many processes. APC methods such as RtR control and FDC are widely applied to detect and compensate for the process variability, and improve yields and reduce manufacturing costs. One of the key challenges is matching process chambers to achieve consistent performance in product quality across the entire toolset. That is, wafers processed in the nominally identical chambers show different end-of-line yield, because the performances of those chambers are different. “Chamber matching”referred to the comparison of the product quality performance of the chamber studied on data from a single or a set of known good chambers [1]. Traditionally, one can monitor changes in process variables and compare the results with a specified target and control limits using SPC. However, not all faults in SPC are related to final quality of the product. In other words, abnormality in many SPC variables does not imply abnormality in QC. More recently, there has been a move toward chamber matching on the manufacturing process through other methods. With VI-probe installation in a reactor of Ti deposition process, Baek et al. [2] noted meaningful differences between good and bad chambers that are classified in terms of end-of-line yield data. Tesauro and Roche [3] used instrumented wafers to identify the causes for chamber mismatching in production in plasma etch systems. Tison [4] applied tool-flow verification methodology to recalibrate the replacement MFC “on-tool” to match the output of the previous MFC. Meanwhile, increasingly, real-time measurements of process variables, such as temperature, pressure, power, voltage, current, flow rate, etc., are available as the

A

NOMENCLATURE F H0 Hα i K Kx i

I. INTRODUCTION

Value of test static. Null hypothesis. Alternative hypothesis. Index of feature variables. Number of sample points. Number of remaining samples of xi after outlier removal. Index of chamber. 25th percentile. 75th percentile. Statistical measure of how well a regression line approximates real data points. Standard deviation. Feature variable of equipment sensor. Mean value of remaining samples.

Manuscript received November 17, 2010; revised March 6, 2011; accepted June 30, 2011. Date of publication September 8, 2011; date of current version June 13, 2012. This work was supported by Natural Science Foundation of Jiangsu Province under Grant SBK201123307, by the National Nature Science Foundation of China under Grant 60904053, and by the Priority Academic Program Development of Jiangsu Higher Education Institutions. This paper was recommended by Associate Editor M. Jeng. T.-H. Pan is with the School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China (e-mail: thpan@ ujs.edu.cn). D. S.-H. Wong and S.-S. Jang are with the Department of Chemical Engineering, National Tsing-Hua University, Hsin-Chu 30013, Taiwan (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMCC.2011.2161669

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manufacturing tool become more sophisticated and expensive. Statistical analysis must be used to identify the critical process variable’s measurements that can be used to chamber performance. In many cases, multivariate statistical analysis must be used to find appropriate combination of variables that can serve the purpose. For example, Davis and Lian [5] performed PCA on sensor-variable data; then, automatic chamber matching can be determined by comparing these PCs with reference PCs associated with a reference chamber. Cherry [6] applied FDA to visualize the differences between chambers in the Fisher space. Despite the effectiveness of the PCA/FDA method in highlighting the differences between chambers from sensor-variable dataset with high dimension and collinearities, it is sometimes difficult to pinpoint the actual key variables. Selection of variables with high loading on the PCs may be error prone as discussed by Cadima and Jolliffe [7]. Ma and colleagues [8] presented multivariate statistical analysis and visualization method that allow one to preliminarily identify the key variables that affect the end-of-line quality of product. In this paper, we focus on an alternative method to quickly diagnose the key variables that cause the difference between chambers using simple statistical data analysis. The central thesis is that while process variable may show substantial differences between golden chambers and inferior chambers, a key process variable that affects product quality must also have sufficient correlation between process variable and product quality. This paper is organized as follows. In the next section, the example of electroplating process that is used to illustrate the proposed chamber-matching procedure is described. In Section III, a simple statistical analysis is introduced to identify golden and inferior chambers using product quality. In Section IV, a set of candidate feature variables that exhibit differences among different tools are identified. Section V shows how to select the key feature variables, which are correlated with the variations in end-of-line quality, from this candidate set. Results of validation experiments will be shown in Section VI. Finally, concluding remarks are given in Section VII. II. EXPERIMENT DESCRIPTION Recently, flip-chip technology has been actively investigated in semiconductor industry because of the demand of increasing inputs/outputs and reducing signal transmission delay. In the flip-chip bumping process, the electroplating method is a good approach to meet fine pitch requirements, especially for high volume production. In this study, development of a performance chamber-matching method for an electroplating process in a local manufacturing facility is presented. Fig. 1 shows the schematic diagram of the process. In the manufacturing process, wafers are placed in a liquid solution (electrolyte). When an electrical potential is applied between a conducting area on the wafer and a counter electrode in the liquid, a chemical redox process takes place that results in the formation of a layer of material on the wafer’s surface [9], [10]. It is known that the uniformity of deposition on the surface of wafer is critical to form round shape bumps in the reflowing process, and affected by

Fig. 1.

Schematic diagram of the electroplating process. TABLE I STATISTICS OF PRODUCT QUALITY FROM DIFFERENT CHAMBERS IN THE FIRST DATASET

several factors such as the quality of electrolyte, anode area and position, temperature of the electrolyte, the electrical conditions during plating, etc. Usually, equipment sensors for tool parameters are done to record raw signal behaviors and to monitor this manufacturing process. To demonstrate our approach, two batches of data are collected (2009/2/23-2009/3/3 and 2009/5/14-2009/5/29) from five normally identical chambers (denoted as CH-A, CH-B, CH-C, CH-D, and CH-E) in a local fabrication unit. The first dataset is used to diagnose the difference between a golden chamber and an inferior chamber, and identify the key variables that affect the final quality of wafer. The second is a validation dataset that checks the result of adjustments that are made during preventive maintenance according to the analysis of the first dataset. These chambers are monitored by ten equipment sensors (which are denoted as {xi }10 i=1 ). At a 1-s sampling rate, every sensor can collect 1–3045 s data depending on the recipe activated. Meanwhile, the uniformity of the electroplated layerprocessed wafer (which is denoted as Y ) can also be measured after the completion of the process. For proprietary reasons, we are not going to reveal the exact values, but present them as arbitrarily scaled values (arbitrary unit, A.U.). III. IDENTIFICATION OF GOLDEN AND POOR CHAMBERS Eighty-two samples were collected and distributed in five chambers as shown in Table I. Before proceeding the parametric statistics, data that satisfy the assumption of normal distribution should be tested. Taking CH-A, for example, the normality test is implemented by MINITAB (which is shown in Fig. 2). It can be seen that the p-value of null hypothesis is 0.476, which is bigger than 0.05, and the assumption is met. Fig. 3 describes the box plot of values of Y . The standard deviations (sn , n = A, B, C, D, E ) of Y in those chambers are

PAN et al.: CHAMBER MATCHING OF SEMICONDUCTOR MANUFACTURING PROCESS USING STATISTICAL ANALYSIS

Fig. 2.

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Normality test for CH-A. Fig. 4.

Profiles of one variable x6 between golden and inferior chambers.

hypothesis H0 and reject Hα [13], [14]. Generally, the cumulative distribution function value of the F -test statistic is an alternative way of expressing the acceptance interval (0, 1 − α) for a one-tailed test. The calculated result “p-value ”can be used to determine which chamber is a chamber that is inferior to CH-A. The lower the p-value, the lower the probability of making an error to label the chamber as an inferior one. As shown in Table I, among the remaining four chambers, only CH-C can be identified as an inferior chamber (using a criterion of p < 0.05). IV. CANDIDATE VARIABLES SELECTIONS

Fig. 3.

Box plots of product quality Y from different chambers (first dataset).

shown in Table I. It seems that the standard deviation of CH-A is smallest among all chambers and can be selected as the golden chamber. The standard F -test [11], [12] is used to determine whether the standard deviations of remaining four chambers are equal to the CH-A, which is defined as H0 : s2n = s2A Hα : s2n > s2A

(1)

where H0 is the null hypothesis, and Hα is the alternative hypothesis; sA and sn (n = B, C, D, E) are the standard deviation of CH-A and the remaining four chambers, respectively. The test static F is given by F =

s2n s2A

(2)

which is assumed to follow the χ2 distribution. The more this ratio deviates from 1, the stronger the evidence for unequal chambers varies. A one-tailed test is implemented here. If value of F is within critical region, hypothesis H0 is rejected and the alternate hypothesis Hα is accepted, which means the two chambers have distinct difference. Otherwise, we should accept

The first step of our procedure is to distinguish which sensor variables exhibit substantial differences between the golden and inferior chambers. The profiles of the 6th sensor variable x6 of all production running in CH-A and CH-C are plotted in Fig. 4. The data trace tells us that the variable may be related to chamber difference and crucial to the wafer quality. However, the dimension of the variable is too large to analyze. Therefore, feature variables, averages, and standard deviations are calculated from the profiles of each sensor [15]. In this example, the time data between 700 and 3000 s are used to extract feature variable according to domain knowledge of an operating engineer. It is well known that statistical tests can be influenced by outliers. A common practice is to introduce a preliminary outlier test such as the popular IQRtest [16], [17] to filter the dataset. For a given data sample, the IQR-test finds the 25th percentile Q1 , the 75th percentile Q3 , and the interquartile range IQR = Q3 − Q1 . Any observation that is outside [Q1 − 1.5 IQR, Q3 + 1.5 IQR] will, then, be removed from the samples. The remaining data are, then, relegated to calculate the feature variables such as means and standard deviations: ⎧ K ⎪ 1 ⎪ 2 ⎪ s = δik (xi [k] − x ¯ i )2 ⎪ x ⎪ Kx i − 1 ⎨ i k =1 (3) K ⎪ ⎪ 1 ⎪ ⎪ ⎪ ¯i = δik xi [k]. ⎩x Kx i k =1

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TABLE II STATISTICS OF SENSOR VARIABLES BETWEEN SENSOR VARIABLES

δik and Kx i are calculated as ⎧ 1 xLi ≤ xi [k] ≤ xUi ⎪ ⎪ ⎪ δ = ⎪ ⎨ ik 0 otherwise ⎪ K ⎪ ⎪ ⎪ δik ⎩ Kx i =

Fig. 5.

Correlation of process variables features with product quality.

(4)

k =1

where K is the number of sample points, and Kx i is the number of remaining samples of xi after outlier removal. i = 1, 2, . . . , 10 is the index of feature variables. Then, F -test is also used to diagnose whether there is a difference in feature variables between CH-A and CH-C. The results of F -test are shown in Table II. It seems that the feature variables x3 , x4 , x6 , x7 , x8 , and x9 are different between the golden and the inferior chambers according to the p-value. V. KEY VARIABLES SECTIONS However, in chamber matching, we want to know not only which of these variables are different, but also which of these variables with difference (candidate variables) have a significant effect on end-of-line quality (key variables). In general, the key variables should give a good explanation of the quality Y . Therefore, the relationship between mean of the candidate variables x ¯i and Y is obtained using linear regression, and the corresponding R2 statistics is calculated. Fig. 5 demonstrates the correlation of four process variables that are examined on product quality. Remaining six process variables are examined in the same way. Then, the R2 versus p-value of all process variables examined are plotted in Fig. 6. It is obvious that the data fall into two categories. A group that includes x6 , x7 , x8 , and x9 has small p-value in the F -test of standard deviations between the golden and inferior chambers, which means that these process variables are less tightly controlled in the inferior chamber, and high R2 , which means that the variations of means of these process variables are related to the product quality. It is found that although standard deviations of x3 and x4 are larger in CH-C than in CH-A, the variations may not be too relevant to product quality.

Fig. 6. Relationship of R 2 versus p-value for all candidate feature variables (first dataset).

Thus, whole chamber-to-chamber matching algorithm can be summarized as follows. Step 1) Acquire product quality and process variable data from more than one chamber. Step 2) Perform the F -test for product quality variations between chambers and identify the golden and inferior chambers. Step 3) Perform the IQR-test for process variables. Step 4) Use F -test to determine the standard deviations of which process variables in the inferior chamber are larger than those in the golden chamber. Step 5) Perform a linear analysis to determine correlation between means of the process variables and product quality. Step 6) Select key variables that have larger standard deviations and sufficient correlation with the product quality.

PAN et al.: CHAMBER MATCHING OF SEMICONDUCTOR MANUFACTURING PROCESS USING STATISTICAL ANALYSIS

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TABLE III STATISTICS OF PRODUCT QUALITY FROM DIFFERENT CHAMBERS IN THE SECOND DATASET

Fig. 8. Box plots of product quality Y from different chambers (second dataset).

of variables between CH-A and CH-C cannot be distinguished. The reason may be that the recipe of those selected key variables (i.e., x6 , x7 , x8 , and x9 ) must be adjusted by field engineers. The conjecture is confirmed by multiple comparison charts [18]. As shown in Fig. 7, the multiple comparison charts can easily characterize and compare which pairs of datasets are significantly different. It is obvious that the values of the four key variables in the second dataset are higher than the first one. This is because the set points of the four variables are increased during the preventive maintenance to increase the value of Y . It also seems that the standard deviations of four variables in the second dataset are smaller than those in the first dataset in CH-C. This means that the performance of controller is improved after preventive maintenance. On the other hand, the values of the uniform thickness are also increased after adjustment, as shown in Fig. 8. It is confirmed again that the selected variables are highly influential to the quality of wafer and validation of the proposed chamber-matching method. VII. CONCLUSION

Fig. 7. Multiple comparison charts for key variables in CH-A and CH-C. (a) Multiple comparison charts for key variables in CH-A. (b) Multiple comparison charts for key variables in CH-C.

VI. VALIDATION To validate the aforementioned method, a second dataset (2009/5/14–2009/5/29) is collected after preventive maintenance during which adjustment of variables x6 , x7 , x8 , and x9 are made. The F -test of product quality is shown in Table III. It seems that there is no significant difference in the product quality variations. Among the five chambers, the importance

In the given example, we have presented a method of performance chamber matching through finding the key variables from the feature variables. Several relationships among electroplating chamber-operating variables are revealed during the evaluation using statistical analysis. It should be pointed out that although the statistical methods employed, e.g., F -test, IQRtest, and linear regression, are not new, the summary of analysis results, which are presented in a chart of R2 versus p-value, allows engineers to visualize them most intuitively. Adoption of this technology not only will help eliminate wasted efforts in utilizing instrumented wafers as quality standards, but also will increase chamber availability due to reduced discrepancies in chamber measurements. Beside chamber qualification, the method can also be used to process monitoring and endpoint detection, identifying the source of a chamber fault. Of course, the best technique to ensure chamber-to-chamber or tool-totool reproducibility is not positively known and may vary by

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Tian-Hong Pan received the B.S. degree from Anhui Agriculture University, Hefei, China, and the M.S. degree from the Gansu University of Technology, Lanzhou, China, in 1997 and 2000, respectively, and the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, Shanghai, China, in 2007. He is currently an Associate Professor with the School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China. His research interests include multiple model approach and its application, machine learning, virtual metrology, predictive control, run-to-run control theory and practice, etc.

David Shan-Hill Wong received the B.S. degree in chemical engineering from the California Institute of Technology, Pasadena, in 1978, and the Ph.D. degree in chemical engineering from the University of Delaware, Newark, in 1982. He has been a Faculty Member with the Department of Chemical Engineering, National TsingHua University, Hsinchu, Taiwan, since 1983. He is actively involved in consulting and collaborative research with chemical process and semiconductor manufacturing industries. His research interests in the area of process system engineering include design and control of energy efficient separation processes and advanced process control in batch-based manufacturing.

Shi-Shang Jang received the M.S. degree from National Taiwan University, Taipei, Taiwan, and the Ph.D. degree from Washington University, St. Louis, MO, both in chemical engineering, in 1980 and 1986, respectively. He has been a Professor with the Department of Chemical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, since 1992. He was the Chairman of the Department from 2000 to 2004. He has been involved in many projects granted by global corporations for recent five years. His research interests include run-to-run control and virtual metrology theory and practice.